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Carbon Nanotubes Carbon Nanotubes Riichiro Saito Riichiro Saito [email protected] [email protected] http://flex.ee.uec.ac.jp http://flex.ee.uec.ac.jp
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Carbon NanotubesRiichiro [email protected]://flex.ee.uec.ac.jp
(5,5)(9,0)(6,5)Carbon NanotubesArmchair NanotubeZigzag NanotubeChiral Nanotube
Solid State Properties of Carbon NanotubesStructures and SymmetryElectronic and Phonon PropertiesRaman IntensitiesTransport PropertiesMagnetic PropertiesApplicationsPhysical Properties of Carbon Nanotubes, by R. Saito, G. Dresselhaus and M.S. Dresselhaus, Imperial College Press (1998) ISBN 1-86094-093-5
Chiral Vectors : (n,m)Chiral Vector (equator of nanotube): OA, ChTranslational Vector of 1D material: OB, TUnit Cell : OABB
SymmetrySymmorphic (mirror symmetry)Armchair Nanotube (n,n), n=mZigzag Nanotube (n,0), m=0Non-Symmorphic (axial chirality)Zigzag Nanotube (n,m), nm
Fig: (a) (5,5) armchair, (b) (9,0) zigzag, and (c) (10,5) chiral nanotubes
Diameter and Chiral AngleDiameter : d
Chiral Angle : zigzag =0armchair =/6chiral 0
Reciprocal Lattice and Wave Vectors1 Dimensional Wave VectorsNanotube axis direction
Discrete in Circumferential Direction
Electronic Properties of Graphene band of graphiteUnit Cell, B. Z.Energy BandZero Gap Semiconductor
Energy Bands of NanotubesN one-dimensional bands(5,5)(9,0)(10,0)
Metal or Semiconductor depending on chiralityDensity of StatesRule for Metal Nanotube
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